Question

In 1986, the worst nuclear disaster occurred in Chernobyl, USSR, when an explosion at a nuclear power plant released 1000 kg of radioactive cesium-137. The following model calculates the remaining amount of cesium-137 in the atmosphere x years after 1986.
F(x)=1000(0.5)x/30
If 100 kg or more of cesium-137 is considered unsafe for humans, when will this area be safe again (you may give an estimate based on your table of values above or find the exact value from a graphing utility)?

What is the y-intercept for this function and what does it represent? Is this a growth or decay function?

Answer 1

Considering the function for the remaining amount of cesium in the atmosphere, F(x) = 1000×0.5^(x/30), we have;

First part:

• The area will be safe again in about 100 years time.

Second part;

• The y-intercept is at the start of the measurement

Third part;

• The function is a decay function

Which method can be used to evaluate the given function?

First part;

The given function for the remaining amount of cesium is presented as follows;

$F(x) = 1000 \times {0.5}^{ \frac{x}{30} }$

When 100 kg. of cesium is remaining, we have;

$100= 1000 \times {0.5}^{ \frac{x}{30} }$

Which gives;

$\frac{x}{30} = \frac{ log(0.1) }{ log(0.5) }$

$x= \frac{ log(0.1) }{ log(0.5) } \times 30 \approx 100$

• Therefore, the area will be safe again in approximately 100 years.

Second part;

The y-intercept is given by the point where x = 0

At the y-intercept, we therefore have;

$F(0) = 1000 \times {0.5}^{ \frac{0}{30} }$

• F(0) = 1000

At the y-intercept, the amount of cesium remaining, F(x) is 1,000, which is the initial amount of cesium.

• The y-intercept is therefore, at the start of the measurement, where 1000 kg. is present in the atmosphere.

Third part;

The amount of cesium remaining F (x) decreases as the time, x, increases, the function is therefore a decay function.

Learn more about exponential functions here;

brainly.com/question/2456547

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